Unconventional High Temperature Superconductivity in Cubic Zinc-blende Transition Metal Compounds

We consider possible high temperature superconductivity (high-T$_c$) in transition metal compounds with a cubic zinc-blende lattice structure. When the electron filling configuration in the d-shell is close to d$^7$, all three t$_{2g}$ orbitals are near half filling with strong nearest neighbor antiferromagnetic (AFM) superexchange interactions. We argue that upon doping, this electronic environment can be one of "genes" to host unconventional high T$_c$ with a time reversal symmetry broken $d_{2z^2-x^2-y^2} \pm i d_{x^2-y^2}$ pairing symmetry. With gappless nodal points along the diagonal directions, this state is a direct three dimensional analogue to the two dimensional $B_{1g}$ d-wave state in cuprates. We suggest that such a case may be realized in electron doped CoN, such as CoN$_{1-x}$O$_x$ and (H, Li)$_{1-x}$CoN.

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